I am currently finding my way into Angband, after some initial trouble I finally got a character rolling on dl21 cl21. He's a Kobold rogue. My question:
I have currently two rings equipped:
A Ring of STR+3, that allows me to get two attacks on my trident of slay orc +6,+4 which has been the best weapon I found so far and a ring of free action. I already read that Free Action is an important power to have but now I also found a ring of rFire and rCold. I am unsure which ring to ditch for now.

Fire/cold resistance are important, but at the depth you were at I wouldn't consider swapping either of your other rings out. Lack of Free Action will get you killed at some point, and Strength rings are really solid in general, between the increased number of blows, increased damage per blow, and having your Strength sustained.

Where you start absolutely needing fire/cold resistance is when monsters start showing up that can breathe large amounts of fire/cold damage. That takes a little while, and if you know which monsters use those attacks, you can just avoid them, especially as a rogue.

Use Fire/Cold while fighting red and white young dragons and the like, until you find armor or shield of resistance, or other similar item. (It won't be long.) But Free Action is much more important until you know the monsters, and damage (STR) is one the three most important stats (HP and speed are the others.)